We considered a four-dimensional scale-invariant effective theory with a torsion field conformally coupled to a metric field. We find that the contribution from the torsion field is negligible in the evolution of the early universe. An exact solution is also obtained for k = 0 Friedmann-Robertson-Walker space in the vanishing cosmological constant limit. This solution is also a good approximation to k not-equal 0 spaces. Possible implications to the inflationary universe are also discussed.